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A local criterion for cleavage fracture of a nuclear pressure vessel steel
Abstract
Experiments were performed on three heats of A508 class 3 steel in order to determine the mechanical conditions for cleavage
fracture. These tests were carried out on various geometries including 4-point bend specimens and axisymmetric notched tensile
bars with different notch radii which have been modelized using the finite element method. In one heat, the temperature range
investigated was from 77 K to 233 K. It is shown that the cleavage resistance is increased by tensile straining. Moreover,
the probability of fracture obeys the Weibull statistical distribution. All the results can be accounted for in terms of a
local criterion based on Weibull theory and which takes into account the effect of plastic strain. In this criterion, the
parameters which were experimentally determined are found to be temperature independent over the range 77 K to 170 K. The
applicability of the approach proposed for cleavage fracture at the crack tip is also examined. It is shown that the experimental
results published in the literature giving the variation of fracture toughness with temperature can be explained by the proposed
criterion which predicts reasonably well both the scatter in the experimental results and theK
ICtemperature dependence.
... The brittle failure of low-alloyed steels is caused by the unstable propagation of a microscopic crack, which appears due to the rupture of a microscopic brittle phase [16][17][18]. Since this phase is often a carbide [19][20][21][22][23], a statistical analysis of the carbide population was carried out to identify its equivalent diameter distribution. ...
... For the probabilistic description of fracture toughness K Jc , the Beremin model is used [16]. In the present paper, only a brief description of this model is presented. ...
... The parameters m and σ u are determined as follows. Due to the low number of experimental fracture toughness results, a usual value of m = 20 is adopted for all materials, which is consistent with the values reported in the literature for RPV steels [16,36,37]. The value of σ u is determined based on the evolution of the median K Jc -which corresponds to the experimental fracture probability P r of 50 %-with test temperatures. ...
The influence of the chemical composition on the brittle fracture behaviour of quenched and tempered low alloy bainitic steels was investigated thanks to the laboratory elaboration of three model alloys which have underwent a heat treatment to improve their chemical homogeneity. Two model materials with chemical compositions simulating zones of large (0.29%C) and intense (0.38%C) positive macrosegregation were characterized and compared with the nominal composition material (0.18%C). The ductile to brittle transition temperatures T56J and T0 of the materials with nominal and large carbon content are similar, whilst those of the material with the highest carbon content are unexpectedly significantly lower. Fractographic analyses indicate that the brittle fracture mechanisms depend also on the chemical composition. For 0.18 and 0.29%C, cleavage is the dominant brittle fracture mechanism, whilst a mix of cleavage and intergranular failure is observed for 0.38%C at the same levels of fracture energy or toughness. When cleavage failure is the dominant mechanism, it often originates at large molybdenum and manganese-enriched carbides located at grain boundaries likely identified as former austenitic grain ones. Microstructural analyses show variations of the large carbide population and ferritic grain size between the three alloys. Also, as carbon content increases, an evolution towards a lower bainite/martensite crystallographic microstructure is observed. The effects of these microstructural differences on the brittle fracture behavior is discussed.
... Welds are prone to manufacturing defects, and to ensure the structural integrity of such a component, the fracture process at defects must be considered. In ferritic steels at low temperatures, brittle failure typically presents as transgranular cleavage failure (Beremin 1983;Wallin 1984). This failure mechanism occurs when a microcrack nucleates from second-phase particles and then propagates in an unstable manner due to high stress. ...
... Ranking here by I wl may be considered more general than ranking by the Weibull stress, as it is valid for any choice of hazard function. If the hazard function in Eq. (2) is replaced by the hazard function of the Beremin model (Beremin 1983), I wl follows from the Weibull stress as ...
The fracture surfaces of 49 SE(B) toughness tests performed on five different geometries, were carefully investigated by SEM imaging and cross-section analysis. The specimens were extracted from a large multi-pass weld in T-S orientation. The failure characteristics were associated with three distinctly different zones of the weld. Transgranular fracture occurred primarily in the reheated zone and in the as-welded zone with a dendritic microstructure inclined relative to the crack plane. With a dendritic microstructure aligned with the crack plane intergranular fracture occurred. The toughness of the as-welded zone with a low inclination angle, was significantly lower than that obtained in the other two weld zones. Due to the relatively large size of the zones compared to the fracture process zones of the tests, it is appropriate to characterize the failure behavior as large-scale heterogeneity. Weakest-link modeling may be applied locally in each weld zone, giving rise to three different sets of model parameters. A new calibration technique is introduced and used to fit a local weakest-link model to the toughness distribution curves of the individual zones.
... Consequently, predictions of the crack initiation are excluded from this analysis. The reason is that the output predictions from models based on the widely accepted weakest-link assumption for crack initiation typically manifest as either the probability of failure under specified loads or the distribution of loads at which failure occurs [1,[67][68][69][70]. The inclusion of crack initiation predictions, which would yield a distribution of crack arrest lengths, fundamentally contradicts our goal of establishing a direct correlation between crack arrest length and loading condition. ...
For pressurized thermal shock of a reactor pressure vessel (RPV), flaw stability is assessed using the fracture mechanics (FM) for a postulated flaw. After long-term operation, neutron irradiation may reduce safety margins in some plants. The Beremin can mitigate the over-conservatism of conventional FM by performing a realistic cleavage fracture assessment. This study explored the coupled model of the Beremin model with the GTN model to establish a more accurate evaluation method for realistic structures experiencing cleavage fracture after a small ductile crack growth in ductile-to-brittle transition temperature region. The parameters of both models were determined using C(T) and SE(B) specimens. These parameter values were used for the coupled model to predict the fracture bounds of critical cleavage fracture of a surface-flawed plate specimen under bending or tensile load resembling constraint of an RPV. Experimental fracture tests at -80°C and -120°C were conducted on flat plates with a surface flaw, revealing that most critical stress intensity factors (K) fell within the predicted bounds. Notably, at -80°C, where small ductile flaws were generated, the coupled model's predictions outperformed those of the Beremin model when compared to test data. Overall, the findings confirm that the coupled model was an appropriate approach for accurately assessing cleavage fractures resulting from small ductile crack growth.
In the development of aluminum casting alloys, considerable attention is given to the impact of various alloying elements, with numerous studies exploring how these elements influence the material’s properties. However, the selection of alloying elements alone does not ensure optimal final quality. The casting process and melt treatment methods also play a critical role in achieving a defect-free structure, particularly when paired with defect characterization and final property assessment. Therefore, it is essential to investigate the interplay between alloying element choice, melt treatment, and defect evaluation in tandem. In this study, copper and magnesium main alloying elements have been chosen along with master alloys of Ti–V–Nb as grain refiners for the aluminum cast alloy. Phase formations have been investigated by simulated phase diagrams. Casting experiments have been done using a tilt pouring method into sand molds, and small bubble degassing equipment has been used to ensure the alloying and melt quality satisfying required mechanical strength. Composition and alloying have been validated by spectral analysis and XRF measurements. Microstructural analyses have been performed by both digital microscopy and scanning electron microscopy. EDS mappings have been carried out for alloying elements distributions. Internal defect distribution and defect structure have been evaluated by computed tomography (CT) scans. Both as-cast and heat-treated specimens have undergone tensile and hardness tests to characterize the mechanical behaviors. CT scans and mechanical behaviors have beencorrelated, and defect metrics have been investigated and classified according to defect surface, defect volumes and projected areas on XY–XZ–YZ planes. Contour maps of defect metrics and tensile properties have been analyzed to generate input to finite element simulations for latter stages studies, and correlation of strength-defect regressions has yielded parametric results to understand structural defects–mechanical performance relations. GTN and Beremin localization models capable of depicting material behavior in the presence of defects have been used to link the experimental and virtual validation assessments. In view of test results, a maximum of 0.125 wt% Nb content in AlMgCu–TiV alloy has been proposed having a tensile strength reaching 300 MPa–7.5% elongation at 0.75% Nb content with grain refinement effect owing to Al–Nb, Al–Ti, Al–V aluminide particles and good dispersion of Nb, Ti, V elements on the microstructure as assessed by EDS mapping. CT scan reconstruction images and metrics have successfully connected tensile strength and elongation with defect volume and defect surface area for the proposed alloy. In this context, the volume and surface area of defects have been evaluated as critical metrics in evaluating the mechanical properties of Al7MgCu1.2 cast alloys. Defect localization and failure point detection during plastic deformation zone have been demonstrated by Beremin model which can lead to future studies leveraging these metrics to validate material strength using damage models such as Gurson, GTN or Beremin for crack initiation and propagation methodologies.
Nuclear energy is highly valued in many countries for its reliability, cleanliness and cost-effectiveness. Ensuring the safe development and utilization of nuclear energy has become crucial for addressing the global energy shortage and mitigating climate change. The reactor pressure vessel (RPV) is exposed to a high-temperature, high-corrosion and high-radiation environment, the RPV materials have a significant impact on the stability and safety of a nuclear power station. In this paper, the effects of long-term high-temperature hot aging on microstructure and mechanical properties of RPV steel, as well as the research progress in embrittlement mechanism and service life prediction, are reviewed. At the same time, the existing problems and further research directions of RPV steel are pointed out.
An elastoplastic calculation of circumferentially notched specimens has been performed using the finite element method. This study has been undertaken in order to define the mechanical state of the specimens when rupture occurs. The numerical solutions compare accurately with experiment and follow the trend of known approximate solutions. These calculations allow the use of these specimens for a systematic study of the effect of stress triaxiality on the various rupture modes.
An analysis of the dynamic behavior of hybrid journal bearings is presented. The analysis accounts for the compressibility of the lubricant in the bearing recesses and supply line. Results show that when the journal is subjected to high frequency excitation the bearing stiffness and damping can change drastically. The behavior is characterized by a “break frequency” beyond which the bearing stiffness increases sharply. This is accompanied by a rapid decrease in bearing damping. It is also shown that the cross-coupling stiffness coefficients are reduced at high excitation frequencies. The asymptotic behavior of the stiffness and damping coefficients is examined at both ends of the frequency spectrum.
Experiments were performed on A508 class 3 steel in order to determine the conditions for cavity formation from elongated
MnS inclusions. Circumferentially notched tensile specimens were employed in order to investigate the effect of negative hydrostatic
pressure. The results of finite element calculations and metallographic observations on polished sections were used to evaluate
the conditions required for cavity initiation. Tests were performed at different temperatures in both longitudinal and short
transverse direction. The results can be explained in terms of a local critical stress independent of temperature. This local
stress is tentatively calculated using an extension of Eshelby’s theory for inclusions proposed by Berveiller and Zaoui.
The stresses round a piled-up group of dislocations are investigated with reference to the initiation of a crack. A crack should form when the group consists of about 1000 dislocations piled up under a stress of the magnitude occurring in a cold-worked metal. The stress system due to the crack is obtained. The crack will have a stable equilibrium length, but this length is likely to be determined by the amount of plastic flow which takes place round the tip of the crack.
Charpy-V and three-point bending tests, coupled with uniaxial tensile tests on unnotched specimens, were carried out to investigate the realtionship between microstructure and cleavage resistance in low-carbon 2Mn-3Cr bainitic steels (C less than 0. 05%). While the influence of microstructure on yield strength has to be viewed mainly in terms of the mean subgrain size, the structural unit controlling cleavage fracture can be identified as the covariant (bainitic) packet whose size d//B is very close to the average unit crack path measured on fractured specimens.
Notched bars, subjected to varying amounts of uniform prestrain, have been fractured over a range of low temperatures, to examine the effects of prestrain on cleavage fracture. The parameter studied mainly has been the local tensile stress required to produce cleavage fracture below the notch and it has been. shown that this is increased by prestrain, although the effect of such strain was to increase the transition temperature. Detailed metallographic examination failed to show any features to which the increase in fracture stress could be primarily ascribed and a new interpretation of ‘plastic work’ energy terms is suggested. Delaminations caused by heavy prestrains are related to grain-boundary weakening and to residual stresses.
Cleavage fracture in steels obeys a critical tensile stress criterion; fracture occurs when a microstructurally determined tensile stress is locally exceeded. As a first approximation, the cleavage of a steel can be regarded as the propagation of a Griffith defect, this defect being provided by a cracked carbide particle. Dimensional considerations show that while being a necessary condition, a critical tensile stress is not sufficient to describe cleavage fracture occurring at the tip of a sharp crack. Ritchie, Knott, and Rice (hereafter referred to as RKR) postulated that the fracture stress must be exceeded over a microstructural ‘characteristic distance’ ahead of the crack tip before a steel will cleave. This model of cleavage fracture was used to predict the temperature dependence of the fracture toughness of mild steel, the predictions being in good agreement with experimental results when the characteristic distance was taken as being equal to two grain diameters. Although originally proposed to explain the cleavage toughness of mild steel, the RKR model has been shown by Parks to be applicable to low-alloy steels as well.
The initiation of cleavage microcracks in two coarse-grained vacuum-melted ferrites containing 0.035 and 0.007 per cent carbon was studied by means of tensile tests carried out between room temperature and -195°c in conjunction with special metallographic procedures. The latter involved surface replication of prepolished tensile specimens at various stages along the stress-strain curve as well as progressive sectioning of such specimens to reveal the internal details. In this way, the roles of carbides, mechanical twinning and slip in the initiation of cleavage were determined. Cleavage microcracks develop in ferrite throughout the strain-hardening portion of the stress-strain curve at subzero temperatures, and are mainly initiated by the cracking of carbides. Twinning does not play an important part in crack initiation in these materials at temperatures down to - 195°c. Although carbides may crack copiously during plastic deformation, they lead to microcracking of the ferrite only when the applied stress is high enough to permit the carbide cracks to act as griffith cracks. A model for microcrack initiation by such carbide cracking is proposed.